A137230 Composite numbers that are divisible by the number of their prime factors (counted with multiplicity).

4, 6, 10, 12, 14, 16, 18, 22, 24, 26, 27, 30, 34, 36, 38, 40, 42, 45, 46, 56, 58, 60, 62, 63, 66, 74, 75, 78, 80, 82, 84, 86, 88, 94, 96, 99, 100, 102, 104, 105, 106, 114, 117, 118, 120, 122, 132, 134, 136, 138, 140, 142, 144, 146, 147, 152, 153, 156, 158, 165, 166

Offset

1,1

Comments

k is a term iff {k == 0 (mod BigOmega(k)) and k NOT prime}.

This sequence is obtained from A074946 by excluding all primes from that sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Factor.

Example

k = 3; not a term because not a prime.
k = 4; a term because satisfies both k == 0 (mod bigomega(k)) and k NOT prime.

Mathematica

Select[Range[200], CompositeQ[#] && Divisible[#, PrimeOmega[#]]&] (* Jean-François Alcover, Nov 11 2016 *)

Prog

(PARI) isok(c) = (c>1) && !isprime(c) && !(c % bigomega(c)); \\ Michel Marcus, Feb 28 2023

Crossrefs

Cf. A001222, A002808, A074946.

Sequence in context: A287342 A309177 A163164 * A369896 A283564 A348005

Adjacent sequences: A137227 A137228 A137229 * A137231 A137232 A137233

Keyword

nonn

Author

William A. Tedeschi, Mar 07 2008

Extensions

Edited by Michel Marcus, Feb 28 2023

Status

approved